Hello again - can you come up with an example of a process changing the phase of a wavefunction? Once done, you will have the answer to your problem.

Wavefunctions can be represented by a phasor in a manner similar to classical waves. The phase of the wave at a point in space and time is the angle the phasor makes to the real-number axis.

the change in phase (between the wave-functions travelling different paths) causes the changes in interference pattern

This is not correct - it is the difference in phase between phasors calculated for different paths that tells us the amount of interference. This is explained in the Feynman lectures I have directed to you to in your other thread.